A magnetic field can be produced by

Options

A. a moving charge
B. a changing electric field
C. none of them
D. both of them.

Answer

To solve the question "A magnetic field can be produced by," we will analyze the options provided and apply the relevant physics concepts.

### Step-by-Step Solution:

1. **Understanding the Question**: The question asks about the sources that can produce a magnetic field. We need to evaluate the options given.

2. **Identify Key Concepts**: The key concept to understand here is the Ampere-Maxwell Law. This law relates the magnetic field to electric currents and changing electric fields.

3. **Ampere-Maxwell Law**: According to the Ampere-Maxwell Law, the line integral of the magnetic field (B) around a closed loop is proportional to the total current (both conduction and displacement current) passing through the loop. Mathematically, it can be expressed as:
\[ \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 (I_{\text{conduction}} + I_{\text{displacement}}) \]
where \( \mu_0 \) is the permeability of free space.

4. **Conduction Current**: The conduction current is produced by moving charges. When charges move, they create a magnetic field around them.

5. **Displacement Current**: The displacement current arises from a changing electric field. According to Maxwell's addition to Ampere's Law, a changing electric field can also produce a magnetic field. The displacement current can be expressed as:
\[ I_{\text{displacement}} = \epsilon_0 \frac{d\Phi_E}{dt} \]
where \( \Phi_E \) is the electric flux.

6. **Conclusion**: From the above analysis, we conclude that a magnetic field can be produced by:
- Moving charges (conduction current)
- Changing electric fields (displacement current)

7. **Final Answer**: Therefore, the correct option is "both of them."